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Counting Hamiltonian cycles in Dirac hypergraphs

Thu
18
Nov
Time Thursday 18 November, 2021 at 13:15 - 14:05
Place MA 356

For 0 ≤ \ell < k, a Hamiltonian \ell-cycle in a k-uniform hypergraph H is a cyclic ordering of the vertices of H in which the edges are segments of length k and every two consecutive edges overlap in exactly \ell vertices.

We show that for all 0 ≤ r < k-1, every Dirac k-graph, that is, a k-graph with minimum co-degree pn for some p>1/2, has (up to a subexponential factor) at least as many Hamiltonian \ell-cycles as a typical random k-graph with edge-probability p.

This improves a recent result of Glock, Gould, Joos, Osthus and Kühn, and verifies a conjecture of Ferber, Krivelevich and Sudakov for all values 0 ≤ r < k-1.

(Joint work with Asaf Ferber and Liam Hardiman.)

Event type: Seminar

Speaker:  Adva Mond, University of Cambridge 

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Maryam Sharifzadeh
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